Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigen 10 A -(¹9) 1 2 a) The characteristic polynomial is p(r) = det(ArI) = r^2+2r+1 b) List all the eigenvalues of A separated by semicolons. 1;1 c) For each of the eigenvalues that you have found in (b) (from smallest to largest) give a basis of eigenv than one vector in the basis for an eigenvalue, write them side by side in a matrix. If there is only one zero vector as an answer for the second eigenvalue. i) Give a basis of eigenvectors associated to the smallest eigenvalue. Ә ? sin (a) a əx 8 C m
Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigen 10 A -(¹9) 1 2 a) The characteristic polynomial is p(r) = det(ArI) = r^2+2r+1 b) List all the eigenvalues of A separated by semicolons. 1;1 c) For each of the eigenvalues that you have found in (b) (from smallest to largest) give a basis of eigenv than one vector in the basis for an eigenvalue, write them side by side in a matrix. If there is only one zero vector as an answer for the second eigenvalue. i) Give a basis of eigenvectors associated to the smallest eigenvalue. Ә ? sin (a) a əx 8 C m
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:ii) If there is another eigenvalue, give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector.
ə
ab
sin (a)
∞
a
əx
f
a
Transcribed Image Text:Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix
1 0
^-(+9)
A =
1
2
a) The characteristic polynomial is
p(r) = det(A — rI) =
r^2+2r+1
b) List all the eigenvalues of A separated by semicolons.
1;1
c) For each of the eigenvalues that you have found in (b) (from smallest to largest) give a basis of eigenvectors. If there is more
than one vector in the basis for an eigenvalue, write them side by side in a matrix. If there is only one eigenvalue, enter the
zero vector as an answer for the second eigenvalue.
i) Give a basis of eigenvectors associated to the smallest eigenvalue.
ə
ab
sin (a)
∞
a Ω
a
əx
f
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